persepsi1ea

2022-02-15

Confusion about properties of linear transformation.

I learned from 3Blue1Brown's Linear Algebra videos that one of the rules for a transformation to be linear is that the origin remains fixed in place after transformation. So if$T\left(x\right)=x+a$ is a given transformation, I know that by inserting $x=0$ , it is not a linear transformation. I am not able to understand what is non-linear about it.

I learned from 3Blue1Brown's Linear Algebra videos that one of the rules for a transformation to be linear is that the origin remains fixed in place after transformation. So if

Layla Humphrey

Beginner2022-02-16Added 11 answers

Because $T(0+0)=a$ , whereas $T\left(0\right)+T\left(0\right)=2a$ , which is different from a (unless $a=0$ , of course). But one should have $T(0+0)=T\left(0\right)+T\left(0\right)$ if T was linear.

monogamab0f

Beginner2022-02-17Added 9 answers

If $a\ne 0,\text{then}\text{}T\left(0\right)\ne 0$ . The transformation is what we call affine, but not strictly linear.